Method and apparatus for distance measuring equipment (DME/normal) using a smoothed concave polygonal pulse shape

ABSTRACT

A method for measuring distance includes transmitting a first pair of RF pulses from an airborne interrogator, where the first pair of RF pulses are temporally separated from each other by a first time interval and each of the RF pulses in the first pair of RF pulses has a first pulse waveform. The method also includes receiving a second pair of RF pulses transmitted by a ground transponder. The RF pulses in the second pair of RF pulses have a second pulse waveform characterized by a smoothed concave polygonal function and/or a smoothed concave hexagonal function. The method further includes determining an elapsed time between transmitting the first pair of RF pulses and receiving the second pair of RF pulses and determining a distance between the airborne interrogator and the ground transponder based on at least the elapsed time.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication No. 61/868,205, filed Aug. 21, 2013, entitled “Method andApparatus for Distance Measuring Equipment (DME/NORMAL) UsingAlternative Pulse Shapes”, both of which are commonly assigned, thedisclosures of which are hereby incorporated by reference in theirentirety.

BACKGROUND OF THE INVENTION

Distance Measuring Equipment (DME) is a pulse ranging system asillustrated in FIG. 18 used to measure the slant range between theairborne interrogator 1804 (typically on an aircraft 1802 or satellite)and the ground transponder 1812 (typically with an antenna 1810 totransmit the pulses). DME is typically categorized as DME/N (Normal) andDME/P (Precision). These two systems use different pulse shapes thatsupport their own operational purposes. The DME/N has been used fortraditional rho/theta as well as for en-route and limited terminal areanavigation (RNA V). On the other hand, the DME/P use is limited to MicroLanding System (MLS) approach and landing applications. Current DMEspecifications do not require a particular pulse shape, but specify theallowable ranges of pulse shape parameters such as rise time, width, andfall time.

The common pulse shape used for DME/N is a Gaussian pulse. The Gaussianpulse has a rise time of 2.5 μs and a narrow spectral density that canbe transmitted up to 1,000 Watts. In turn, the typical DME/P pulse shapeis the Cos/Cos² pulse. The Cos/Cos² pulse has a much faster rise timethan the Gaussian pulse, which provides the much higher range accuracy.However, this higher accuracy comes at the expense of the increasedspectral density, which limits its transmission power to 100 Watts toprevent interference on adjacent channels. Thus, the coverage of theDME/P ground station is substantially smaller than that of a DME/Nground station.

Therefore, there is a need in the art for improvements in DME systems.

SUMMARY OF THE INVENTION

This present invention relates generally to ranging systems. Moreparticularly, the invention provides a method and apparatus for DistanceMeasuring Equipment/Normal (DME/N) using alternative pulse waveforms.Merely by way of example, the invention has been applied to methods andsystems that provide improved range accuracy over standard Gaussianpulse waveforms without a loss of coverage.

According to an embodiment of the present invention, an alternativeDME/N pulse shape is utilized that provides much higher range accuracythan the conventional Gaussian pulse shape, and at the same time, hasspectral density characteristics such that it does not causeinterference to adjacent channels even when it is transmitted at thesame high power of 1,000 Watts as the traditional Gaussian pulse.

As described herein, an alternative DME pulse waveform is provided bysome embodiments is compliant with the pulse shape requirements in thecurrent DME specifications to maintain the compatibility with existingDME ground transponders and avionics.

According to an embodiment of the present invention, a method ofmeasuring distance is provided. Merely by way of example, the inventionhas been applied to a method. The method includes transmitting a firstpair of RF pulses from an airborne interrogator, wherein the RF pulsesin the first pair of RF pulses are temporally separated from each otherby a first time interval, and each of RF pulses in the first pair of RFpulses has a first pulse waveform; receiving, at the airborneinterrogator, a second pair of RF pulses transmitted by a groundtransponder after the ground transponder has received the first pair ofRF pulses transmitted by the airborne interrogator, wherein the RFpulses in the second pair of RF pulses are temporally separated fromeach other by a second time interval, and each of the RF pulses in thesecond pair of RF pulses has a second pulse waveform characterized by asmoothed concave hexagonal function, wherein the hexagonal function ischaracterized by a first segment having a first positive slope, a secondflat segment, a third segment having a second negative slope, a fourthsegment having a third negative slope, and a fifth segment having afourth negative slope, an absolute value of the third negative slopebeing less than an absolute value of the second negative slope;determining an elapsed time between transmitting the first pair of RFpulses and receiving the second pair of RF pulses; and determining adistance between the airborne interrogator and the ground transponderbased on at least the elapsed time.

According to an embodiment of the present invention, a method ofmeasuring distance is provided. Merely by way of example, the inventionhas been applied to a method. The method includes receiving, at a groundtransponder, a first pair of RF pulses transmitted from an airborneinterrogator, wherein the RF pulses in the first pair of RF pulses aretemporally separated from each other by a first time interval, andwherein each of the RF pulses in the first pair of RF pulses has a firstpulse waveform; and transmitting, at the ground transponder and afterreceiving the first pair of RF pulses, a second pair of RF pulses,wherein the RF pulses in the second pair of RF pulses are temporallyseparated from each other by a second time interval, and each of the RFpulses in the second pair of RF pulses has a second pulse waveformcharacterized by a smoothed concave polygonal function, wherein thepolygonal function is characterized by at least a first segment having afirst positive slope, a second flat segment, a third segment having asecond negative slope, and a fourth segment having a third negativeslope, and a fifth segment having a fourth negative slope, an absolutevalue of the third negative slope being less than an absolute value ofthe second negative slope; whereby the second pair of RF pulses isreceived by the airborne interrogator, and a distance between theairborne interrogator and the ground transponder is determined based onat least an elapsed time between transmitting the first pair of RFpulses and receiving the second pair of RF pulses.

According to an embodiment of the present invention, a method ofmeasuring distance is provided. Merely by way of example, the inventionhas been applied to a method. The method includes receiving, at a groundtransponder, a first pair of RF pulses transmitted from an airborneinterrogator, wherein the RF pulses in the first pair of RF pulses aretemporally separated from each other by a first time interval, andwherein each of the RF pulses in the first pair of RF pulses has a firstpulse waveform; and transmitting, at the ground transponder and afterreceiving the first pair of RF pulses, a second pair of RF pulses,wherein the RF pulses in the second pair of RF pulses are temporallyseparated from each other by a second time interval, and each of the RFpulses in the second pair of RF pulses has a second pulse waveformcharacterized by a smoothed concave polygonal function, wherein thepolygonal function is characterized by at least a first segment having afirst positive slope, a second flat segment, a third segment having asecond negative slope, and a fourth segment having a third negativeslope, and a fifth segment having a fourth negative slope, an absolutevalue of the third negative slope being less than an absolute value ofthe second negative slope; whereby the second pair of RF pulses isreceived by the airborne interrogator, and a distance between theairborne interrogator and the ground transponder is determined based onat least an elapsed time between transmitting the first pair of RFpulses and receiving the second pair of RF pulses.

According to another embodiment of the present invention, a system fordistance measuring is provided. Merely by way of example, the systemincludes an airborne interrogator operable to transmit a first pair ofRF pulses, wherein the RF pulses in the first pair of RF pulses aretemporally separated from each other by a first time interval, and eachof the RF pulses in the first pair of RF pulses has a first pulsewaveform; and a ground transponder operable to receive the first pair ofRF pulses transmitted by the airborne interrogator, and to transmit asecond pair of RF pulses after receiving the first pair of RF pulses,wherein the RF pulses in the second pair of RF pulses are temporallyseparated from each other by a second time interval, and each of the RFpulses in the second pair of RF pulses has a second pulse waveformcharacterized by a smoothed concave polygonal function, wherein thepolygonal function is characterized by at least a first segment having afirst positive slope, a second flat segment, a third segment having asecond negative slope, and a fourth segment having a third negativeslope, and a fifth segment having a fourth negative slope, an absolutevalue of the third negative slope being less than an absolute value ofthe second negative slope; wherein the airborne interrogator is furtheroperable to receive the second pair of RF pulses transmitted by theground transponder, whereby a distance between the airborne interrogatorand the ground transponder is determined based on at least an elapsedtime between transmitting the first pair of RF pulses and receiving thesecond pair of RF pulses.

According to an embodiment of the present invention, a method ofmeasuring distance is provided. Merely by way of example, the inventionhas been applied to a method. The method includes transmitting a firstpair of RF pulses from an airborne interrogator, wherein the RF pulsesin the first pair of RF pulses are temporally separated from each otherby a first time interval, and wherein each of the RF pulses in the firstpair of RF pulses has a first pulse waveform; receiving, at the airborneinterrogator, a second pair of RF pulses transmitted by a groundtransponder after the ground transponder has received the first pair ofRF pulses transmitted from the airborne interrogator, wherein the RFpulses in the second pair of RF pulses are temporally separated fromeach other by a second time interval, and wherein each of the RF pulsesin the second pair of RF pulses has a second pulse waveformcharacterized by an a filtered asymmetric Gaussian function; determiningan elapsed time between transmitting the first pair of RF pulses andreceiving the second pair of RF pulses; and determining a distancebetween the airborne interrogator and the ground transponder based on atleast the elapsed time.

According to an embodiment of the present invention, a method ofmeasuring distance is provided. Merely by way of example, the inventionhas been applied to a method. The method includes transmitting a firstpair of RF pulses from an airborne interrogator, wherein the RF pulsesin the first pair of RF pulses are temporally separated from each otherby a first time interval, and wherein each of the RF pulses in the firstpair of RF pulses has a first pulse waveform; receiving, at the airborneinterrogator, a second pair of RF pulses transmitted by a groundtransponder after the ground transponder has received the first pair ofRF pulses transmitted by the airborne interrogator, wherein the RFpulses in the second pair of RF pulses are temporally separated fromeach other by a second time interval, and wherein each of the RF pulsesin the second pair of RF pulses has a second pulse waveformcharacterized by a smoothed trapezoidal function, wherein thetrapezoidal function is characterized by a first segment having a firstpositive slope, a second flat segment, and a third segment having asecond negative slope, an absolute value of the first positive slopebeing greater than an absolute value of the second negative slope;determining an elapsed time between transmitting the first pair of RFpulses and receiving the second pair of RF pulses; and determining adistance between the airborne interrogator and the ground transponderbased on at least the elapsed time.

According to another embodiment of the present invention, a system fordistance measuring is provided. Merely by way of example, the systemincludes an airborne interrogator operable to transmit a first pair ofRF pulses, wherein the RF pulses in the first pair of RF pulses aretemporally separated from each other by a first time interval, and eachof the RF pulses in the first pair of RF pulses has a first pulsewaveform; and a ground transponder operable to receive the first pair ofRF pulses transmitted by the airborne interrogator, and to transmit asecond pair of RF pulses after receiving the first pair of RF pulses,wherein the RF pulses in the second pair of RF pulses are temporallyseparated from each other by a second time interval, and each of the RFpulses in the second pair of RF pulses has a second pulse waveformcharacterized by a waveform function, the waveform function including afiltered asymmetric Gaussian function or smoothed trapezoidal function;wherein the airborne interrogator is further operable to receive thesecond pair of RF pulses transmitted by the ground transponder, wherebya distance between the airborne interrogator and the ground transponderis determined based on at least an elapsed time between transmitting thefirst pair of RF pulses and receiving the second pair of RF pulses.

According to another embodiment of the present invention, a system isprovided. The system includes a processor and a computer readable mediumcoupled to the process. The computer readable medium can compriseinstructions that cause the processor to implement a method. The methodmay include one or more methods described herein.

Numerous benefits are achieved by way of the present invention overconventional techniques. For example, embodiments of the presentinvention provide the compatibility with legacy DME avionics and groundtransponder, noise suppression, multipath resistance, and uncompromisedservice coverage area. These and other embodiments of the inventionalong with many of its advantages and features are described in moredetail in conjunction with the text below and attached figures.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a Gaussian pulse shape used in a conventionalDistance Measuring Equipment/Normal (DME/N) and a Cos/Cos² pulse shapeused in a conventional Distance Measuring Equipment/Precision (DME/P).

FIG. 2 illustrates power spectra of a Gaussian DME/N pulse and aCos/Cos² DME/P pulse against a DME spectrum envelope mask.

FIG. 3 illustrates a filtered asymmetric Gaussian pulse shape for DME/Naccording to an embodiment of the invention.

FIG. 4 illustrates a smoothed trapenoidal pulse shape for DME/Naccording to an embodiment of the invention.

FIG. 5 illustrates a smoothed concave hexagonal pulse shape for DME/Naccording to an embodiment of the invention.

FIG. 6 is a simplified flowchart illustrating a method of searching fora candidate alternative pulse shape for DME/N according to an embodimentof the invention.

FIG. 7 is a simplified flowchart illustrating a method of searching fora candidate assymetric Gaussian pulse shape for DME/N according to anembodiment of the invention.

FIG. 8 is a simplified flowchart illustrating a method of searching fora candidate smoothed trapezoidal pulse shape for DME/N according to anembodiment of the invention.

FIG. 9 is a simplified flowchart illustrating a method of searching fora candidate smoothed concave hexagonal pulse shape for DME/N accordingto an embodiment of the invention.

FIG. 10 illustrates a comparison between three examplary alternativepulse shapes and a Gaussian pulse shape according to embodiments of theinvention.

FIG. 11 illustrates time-of-arrival errors as a function of multipathdelay for three examplary alternative pulse shapes according toembodiments of the invention.

FIG. 12 illustrates power spectra of a Gaussian pulse and of a smoothedconcave hexagonal DME/N pulse against a DME spectrum envelope mask,according to an embodiment of the invention.

FIG. 13 is a simplified flowchart illustrating a method of measuringdistance according to an embodiment of the invention.

FIG. 14 is a simplified flowchart illustrating a method of measuringdistance according to another embodiment of the invention.

FIG. 15 is a simplified flowchart illustrating a method of measuringdistance according to a specific embodiment of the invention.

FIG. 16 is a simplified flowchart illustrating a method of measuringdistance according to another specific embodiment of the invention.

FIG. 17 is a simplified flowchart illustrating a method of measuringdistance according to a further specific embodiment of the invention.

FIG. 18 illustrates a simplified system of an airborne interrogator andground transponder according to an embodiment of the invention.

DETAILED DESCRIPTION OF THE SPECIFIC EMBODIMENTS

This present invention relates generally to ranging systems. Moreparticularly, the invention provides a method and apparatus for DistanceMeasuring Equipment/Normal (DME/N) using alternative pulse waveforms.Merely by way of example, the invention has been applied to methods andsystems that provide improved range accuracy over standard Gaussianpulse waveforms without a loss of coverage. Some embodiments of thepresent invention provide improved range accuracy over the standardGaussian pulse waveform without a loss of coverage.

The Distance Measuring Equipment (DME, DME/Normal) based navigationmethod known as DME/DME positioning has been proposed as one of thepossible Alternative Position, Navigation, and Timing (APNT) servicesfor aviation during the outage of the Global Navigation SatelliteSystems. A DME interrogator measures the slant range to a DMEtransponder by means of the elapsed time in exchanging a pair of DMEpulses. Typically, the DME pulse is a Gaussian pulse, and the achievableDME ranging accuracy is primarily determined by the pulse shape.Embodiments of the present invention utilize an alternative DME pulsewaveform that is able to provide much higher range accuracy than theconventional Gaussian pulse. The alternative pulse waveform is compliantwith the pulse shape requirements in the current DME specifications tomaintain the compatibility with existing DME ground transponders andavionics. This alternative DME pulse also takes into account thespectral density characteristics so that it does not cause interferenceto adjacent channels, even when it is transmitted at the same high powerof 1,000 Watts as the traditional Gaussian pulse. Herein, the designapproaches used to determine the alternative DME pulse shape aredescribed and the improvement of range accuracy and multipath mitigationis compared to the traditional Gaussian pulse. In addition,implementation of the alternative pulse in the existing transponders andavionics is discussed.

The Federal Aviation Administration (FAA) has recently initiated anAlternative Position, Navigation, and Timing (APNT) program to maintainsafe air traffic control operations during the possible outage of GlobalNavigation Satellite Systems (GNSS). One of the APNT architecturesproposed by the FAA is based on DME/DME (DME/N) positioning thatutilizes two or more DME ground transponders as ranging sources toenable horizontal navigation. The alternative DME/N pulse provided byembodiments of the present invention enables DME/DME positioning, meetsDME spectrum requirements, and maintains compatibility with existing DMEairborne interrogators.

DME/N Pulse Requirements

The DME/N pulse shape requirements largely consist of the pulse shapeparameters and spectral density. The DME/N pulse shape requirements ofthe ground transponder are listed in Table 1. The rise time is the timerequired to rise from 10% to 90% of the peak voltage amplitude in theleading edge. The fall time is the time required to fall from 90% to 10%of the peak voltage amplitude in the trailing edge. The pulse durationis the time between the points of 50% of the peak voltage amplitude inthe leading and trailing edges.

TABLE 1 DME/N Ground Transponder Pulse Shape Requirements Pulse ShapeParameters Range Rise Time 2.5 (+0.5, −1.0) μs Pulse Top Noinstantaneous fall below a value which is 95% of the maximum voltageamplitude of the pulse Pulse Duration 3.5 (±0.5) μs (width) Fall Time2.5 (±0.5) μs

The DME RF pulse signal spectrum requirement is as follows:

RF Pulse Signal Spectrum: The spectrum of the pulse modulated signal issuch that during the pulse, the effective radiated power contained in a0.5 MHz band centered on frequencies 0.8 MHz above and 0.8 MHz below thenominal channel frequency in each case does not exceed 200 mW (23 dBm),and the effective radiated power contained in a 0.5 MHz band centered onfrequencies 2 MHz above and 2 MHz below the nominal channel frequency ineach case does not exceed 2 mW (3 dBm). The effective radiated powercontained within any 0.5 MHz band decreases monotonically as the bandcenter frequency moves away from the nominal channel frequency.

The Effective Radiated Power (ERP) is defined as the product of thepower supplied to the antenna and the antenna gain relative to a halfwave dipole in a given direction. The power supplied to the antenna inthe requirement is the average power in a 0.5 MHz frequency bandcentered on either ±0.8 MHz or ±2 MHz away from the center frequency ofa DME channel. Then, the ERP, P_(ERP), can be formulated as follows:P _(ERP) =P _(Avg) +G _(Ant)+EIRP_(Conv) +L _(Cable) +D in dB  (1)where P_(Avg) is the average transmission power in an interestedfrequency band, G_(Ant) is an antenna gain, EIRP_(Conv) is theconversion factor between ERP and Effective Radiated Isotropic Power(EIRP), L_(Cable) is a cable loss from the DME transmitter to anantenna, and D is the duty cycle factor that is the ratio of averagepower to peak power. Given the operational values of those parametersand the allowed P_(ERP), the maximum average transmission power in theinterested frequency band, P_(Thr), can be determined from solvingequation (1).

Table 2 shows sample calculations of P_(Thr) in the two designatedfrequency bands with typical DME operational values of the parameters inequation (1). Note that the duty cycle factor is based on the peak powerof 1,000 watts and Pulse Repetition Frequency (PRF) of 4,800 pulse pairsper second (ppps). P_(Thr) in Table 2 will be used as the threshold ofan average transmission power in the given frequency bands in searchingfor an alternative DME/N pulse assuming that the alternative pulse isused in the same operation conditions.

TABLE 2 Sample Calculations of Allowable Transmission Power Across GivenFrequency Band Offset from Center Frequency ±0.8 MHz ±2 MHz P_(ERP)(dBm) 23 3 G_(Ant) (dB) 9 9 EIRP_(Conv) (dBi) −2.15 −2.15 L_(Cable) (dB)−2.6 −2.6 D (dB) with peak 16.21 16.21 power = 1000 watt and PRF = 4800ppps P_(Thr) (dBm) 2.54 −17.5

Gaussian DME/N Pulse Shape and Spectral Density

A Gaussian DME/N pulse is a commonly used DME/N pulse and can beformulated as follows

$\begin{matrix}{{f( {t,\mu,\sigma} )} = {\mathbb{e}}^{- \frac{{({t - \mu})}^{2}}{2\sigma^{2}}}} & (2)\end{matrix}$where t is time, μ is the mean time when the peak voltage amplitudeoccurs, and σ is the standard deviation of the pulse. FIG. 1 shows aGaussian DME/N pulse having 2.5 μs rise and fall time and 3.5 μs width.The amplitude of the Gaussian pulse in FIG. 1 represents normalizedvoltages. In DME/N operation, the interrogation pulse is coded in pairswith a nominal spacing of 12 μs (X mode) or 36 μs (Y mode). The replypulse is coded in pairs with a nominal spacing of 12 μs (X mode) or 30μs (Y mode). The spacing is defined as the time duration between the 50%points of the peak amplitude at the leading edges in the first and thesecond pulses. FIG. 1 also shows Cos/Cos² DME/P pulse for comparison.

The DME spectrum requirement is based on the average power or channelpower. Designating s(f) as the spectral density of the Gaussian pulsef(t), the average power within a given frequency band is computed from

$\begin{matrix}{{P_{avg}( {{f\; 1},{f\; 2}} )} =  {\frac{1}{f_{2} - f_{1}}\int_{f\; 1}^{f\; 2}} \middle| {s(f)} \middle| {}_{2}\ {\mathbb{d}f} } & (3)\end{matrix}$where f₁ and f₂ are the minimum and the maximum frequencies in the givenfrequency band. P_(avg) within 0.5 MHz frequency band at ±0.8 MHz or ±2MHz are approximately −36 dBm and −43 dBm, respectively. P_(avg) is muchlower than P_(Thr), therefore we can see that the ideal Gaussian DME/Npulse has sufficient spectrum margins.

Although the DME spectrum requirement uses the channel power at the twogiven frequencies, it is more intuitive to compare the power spectrum,rather than the power spectrum density, of a pulse against a spectrumenvelope mask to check the overall compliance of the spectrumrequirement. FIG. 2 shows the power spectrums (dBm) of the GaussianDME/N pulse and Cos/Cos² DME/P pulse with the DME spectrum envelopemask. The peak pulse power transmission is assumed to be 1,000 Watts (60dBm). In FIG. 2, the power spectrum of the Gaussian pulse shows asignificant margin against the spectrum envelope mask, but the Cos/Cos²DME/P pulse exceeds the mask in several frequencies. Note that theenvelope mask is not a requirement but a practical representation of theminimum power spectrum attenuation over the frequencies.

Alternative DME/N Pulse Shapes

The inventor has considered multiple factors in developing analternative DME/N pulse. First, the targeted DME/N pulse should providesignificant ranging accuracy improvement enough to motivate theimplementation of the alternative pulse. Second, the pulse shape shouldcomply with the DME/N pulse shape requirement in Table 1 to be processedwithout changes in DME transponder or avionics. Third, the spectrum ofthe alternative pulse should be narrow enough to allow a hightransmission power up to 1,000 Watts without violating the DME spectrumrequirement. The existing DME transponder with the standard Gaussianpulse typically broadcasts replies with 1,000 Watts peak power.

One or more of these factors may be implemented in the alternative DME/Npulse shapes to improve a standard Gaussian DME/N pulse shape andspectral density. For example, the alternative DME/N pulse shapes maybroadcast replies the 1,000 Watt transmission power with minimalinterference between adjacent channels. The power spectrum and/orfrequency domain of the pulse may be relatively narrow to minimize theinterference between the channels. The alternative DME/N pulse shapesmay also include a specified right leading-edge rise time, duration, andfall time that meet the DME specification and power spectrumrequirements. In some embodiments, the noise (e.g., through thespecified rise time) and a multipath impact may be mitigated, so thatthe combination of the rise time, fall time, power, and the ability tomitigate the noise through these aspects provides improved alternativeDME/N pulse shapes.

The use of the alternative DME/N pulse shapes also offer severalimprovements over other systems. For example, at least some of thealternative DME/N pulse shapes may travel at least 200 nautical milesthrough the use of the 1,000 Watt transmission power. The power spectrumof the pulse may be implemented to provide little to no interferencebetween channels, allowing the pulses to travel significant distances(e.g., approximately 100 nautical miles) between DME/N ground stations.

Methodology in Searching for Alternative DME/N Pulse Shapes

The inventor has determined that three different alternative DME/Npulses can be utilized in conjunction with embodiments of the presentinvention: asymmetric Gaussian pulse (AGP), smoothed trapezoidal pulse(STP), and smoothed concave hexagonal pulse (SCP).

Filtered or Unfiltered Asymmetric Gaussian Pulse (AGP)

An asymmetric Gaussian pulse (AGP) has different standard deviations (σ)in the left and right sides (i.e., the rising edge and the falling edge,respectively) of the distribution. An asymmetric normalized Gaussianpulse shape can be formulated as follows:

$\begin{matrix}{{g( {x,\mu,\sigma_{1},\sigma_{2}} )} = \{ \begin{matrix}{\mathbb{e}}^{- \frac{{({x - \mu})}^{2}}{2\sigma_{L}^{2}}} & {{{{{if}\mspace{14mu} x} \leq \mu},}\mspace{14mu}} \\{\mathbb{e}}^{- \frac{{({x - \mu})}^{2}}{2\sigma_{R}^{2}}} & {{otherwise}.}\end{matrix} } & (4)\end{matrix}$Since the asymmetric Gaussian pulse should comply with the pulse widthdefined at the half amplitude, the relationship between σ_(L) and σ_(R)can be formulated using the following process. First, take μ=0 and thepeak amplitude of the pulse as one for a simplified equation. Definingx_(L,1/2) the time corresponding to the half amplitude point of the lefthand side Gaussian pulse, then

$\begin{matrix}{{\mathbb{e}}^{- \frac{x_{L,{1\text{/}2}}^{2}}{2\sigma_{L}^{2}}} = {\frac{1}{2}.}} & (5)\end{matrix}$Rearranging (5) for x_(L,1/2) is

$\begin{matrix}{x_{L,{1\text{/}2}} = {- {\sqrt{{- 2}\mspace{14mu}{\ln( \frac{1}{2} )}\sigma_{L}^{2}}.}}} & (6)\end{matrix}$Next, the width of the pulse is defined asW=x _(R,1/2) −x _(L,1/2)  (7)where x_(R,1/2) is the time corresponding to the half amplitude point ofthe right hand side of the Gaussian pulse as below

$\begin{matrix}{x_{R,{1\text{/}2}} = {\sqrt{{- 2}\mspace{14mu}{\ln( \frac{1}{2} )}\sigma_{R}^{2}}.}} & (8)\end{matrix}$Inserting equation (6) and (8) to (7), σ_(R) can be formulated asfollows

$\begin{matrix}{\sigma_{R} = {\frac{W + {\sigma_{L}\sqrt{{- 2}\mspace{14mu}{\ln( \frac{1}{2} )}}}}{\sqrt{{- 2}\mspace{14mu}{\ln( \frac{1}{2} )}}}.}} & (9)\end{matrix}$Using the relationship in (9), σ_(L) and W can be varied to find acandidate set of the targeted alternative DME/N pulse. After combiningthe two Gaussian pulses, it may be necessary to round the peak of theresultant asymmetric Gaussian pulse by using a smoothing filter when theslopes of the two Gaussian distribution are largely different and make anear discontinuity. In some embodiments, the smoothing filter may createa filtered asymmetric Gaussian pulse (“filtered asymmetric Gaussianpulse” and “asymmetric Gaussian pulse” are used interchangeably). Therange of W is from 3.0 μs to 4.0 μs as listed in Table 1. With the rangeof W, σ_(L) from 0.77 μs to 1.77 μs could generate a large set of AGPthat meets the DME pulse shape and spectrum requirements. The range ofσ_(R) may be from 0.90 μs to 1.78 μs according to embodiments of theinvention.

One example of an AGP having σ_(L)=0.86 μs and σ_(R)=1.66 μs is shown inFIG. 3 according to an embodiment. Its rise time, width, and fall timeis 1.57 μs, 3.06 μs, and 2.81 μs, respectively. It should be noted thatother values of σ_(L) and σ_(R) may be used according to otherembodiments of the invention. One of ordinary skill in the art wouldrecognize many variations, alternatives, and modifications. In someembodiments, σ_(L) is in a range from about 0.77 μs to about 1.0 μs.

Smoothed Trapezoidal Pulse (STP)

According to another embodiment of the present invention, a trapezoidalpulse is used as a baseline pulse shape as shown in FIG. 4, whichillustrates a smoothed trapenoidal pulse shape for DME/N according to anembodiment of the invention. The baseline trapezoidal pulse Waveform ischaracterized by a first segment defined by coordinates (X1, 0) and (X2,1), a Second segment defined by coordinates (X2, 1) and (X3, 1), and athird segment defined by Coordinates (X3, 1) and (X4, 0). The firstsegment has a first positive slope; the second segment is flat; and thethird segment has a second negative slope.

The sharp corners of the baseline trapezoidal pulse would result inexcessive spectral energy in high frequency region that may not meet theDME spectrum requirement although the baseline pulse could meet the DMEpulse shape requirement. Therefore, a smoothing filter can be used toround the sharp corners of the baseline trapezoidal pulses such that thesmoothed pulses have sufficient low powers at the frequencies beyond thecenter frequency region of a DME. According to some embodiments, thesmoothing filter may be a moving average filter, a spline filter, a zerophase forward and backward digital filter, or the like.

The pulse design parameters are the locations of X1, X2, X3, X4, and thelength of the smoothing window. (Note that Y1=0, Y2=1, Y3=1, and Y4=0,for a normalized pulse amplitude.) FIG. 4 shows one particular smoothedtrapezoidal pulse (STP) having a rising time of 1.50 μs, a fall time of2.13 μs, and pulse width of 3.04 μs according to an embodiment of theinvention. It should be noted that other values of X1, X2, X3, and X4may be used according to other embodiments of the invention. One ofordinary skill in the art would recognize many variations, alternatives,and modifications. In some embodiments, X1 may be defined to be 0without losing generality. X2 may be in a range from about 1 μs to about3 μs; X3 may be in a range from about 1.5 μs to about 5.1 μs; and X4 maybe in a range from about 3.6 μs to about 7.0 μs. In some embodiments,the first segment of the baseline trapezoidal pulse waveform has apositive slope that is greater than about 0.7 μs⁻¹.

Smoothed Concave Hexagonal Pulse (SCP)

According to yet another embodiment of the present invention, a smoothedconcave hexagonal pulse is utilized. In some ways similar to thetrapezoidal pulse, the baseline pulse has a concave shape and additionaldegrees of freedom. The concave hexagon in FIG. 5 is presented as anexample and shows a preferred hexagonal shape. The baseline concavehexagonal pulse waveform is characterized by a first segment defined bycoordinates (X1, Y1) and (X2, Y2), a second segment defined bycoordinates (X2, Y2) and (X3, Y3), a third segment defined bycoordinates (X3, Y3) and (X4, Y4), a fourth segment defined bycoordinates (X4, Y4) and (X5, Y5), and a fifth segment defined bycoordinates (X5, Y5) and (X6, Y6). In a particular implementation, thefirst segment has a first positive slope; the second segment is flat;the third segment has a second negative slope; and fourth segment has athird negative slope; and the fifth segment has a fourth negative slope.The absolute value of the third negative slope is less than the absolutevalue of the second negative slope, thereby giving rise to the concavehexagonal shape. The pulses generated from the concave hexagonal shapewould have a narrow width around the peak that could help easily detectthe peak of the first pulse (direct), thus mitigate multipath impactsexcept for very short delay multipath. A similar concave polygon withadditional degrees of freedom can be used according to other embodimentsof the invention.

The sharp corners of the baseline concave hexagonal pulse are rounded byusing a smoothing filter to reduce power in the high frequency region insome implementations. The smoothed concave hexagonal pulse illustratedin FIG. 5 has a rise time of 1.56 μs, a fall time of 2.30 μs, and pulsewidth of 3.06 μs according to an embodiment of the invention. It shouldbe noted that other values of (X1, Y1), (X2, Y2), (X3, Y3), (X4, Y4),(X5, Y5), and (X6, Y6) may be used according to other embodiments of theinvention. One of ordinary skill in the art would recognize manyvariations, alternatives, and modifications. In some embodiments, X1 maybe defined to be 0 without losing generality. X2 may be in a range fromabout 1 μs to about 3 μs; X3 may be in a range from about 1 μs to about3.8 μs; X4 may be in a range from about 1.1 μs to about 4.7 μs; X5 maybe in a range from about 3.5 μs to about 5.32 μs; and X6 may be in rangefrom about 3.9 μs to about 7.72 μs. Y1 and Y6 may be defined to be 0,and Y2 and Y3 may be defined to be 1 for a normalized pulse amplitude.In some embodiments, Y4 may be in a range from about 0.5 to about 1; andY5 may be about 0.5. In some embodiments, the first segment of thebaseline concave hexagonal pulse waveform has a positive slope that isgreater than about 0.7 μs⁻¹. In other embodiments, the absolute value ofthe second negative slope is greater than about 0.7 μs⁻¹.

The alternative pulses described above were generated from following theprocedures in FIG. 6. The optimal alternative pulse can be defined asthe pulse that yields the minimum error in measuring time of arrivalunder noise and multipath while complying with the pulse shaperequirement and the spectrum requirement given a transmission power of1,000 Watts (60 dBm). The optimal pulses are designed to accommodate 10dB margin or more against the spectrum thresholds at 0.8 MHz and 2 MHzto compensate for possible limitations of the DME transponder and/oravionics in implementing the pulses.

FIG. 6 is a simplified flowchart illustrating a method of computing analternative pulse waveform for DME/N according to an embodiment of theinvention. At 602, the system determines the ranges of parameters forthe pulse waveform under consideration. At 604, one or more parametervalues are changed within the determined ranges. At 606, the systemchecks whether the resultant pulse waveform meets the pulse shaperequirements. If the answer is “no,” the system loops back to 604 whereone or more parameters are changed. If the answer is “yes,” at 608, thesystem checks whether the resultant pulse waveform meets the spectrumrequirements. If the answer is “no,” the system loops back to 604 whereone or more parameters are changed. If the answer is “yes,” at 610, thesystem evaluates the range accuracy and multipath performance of theDME/N using the resultant pulse waveform. At 612, the system determinesthe ranges of signal-to-noise ratio (SNR) and multipath parameters(e.g., the peak amplitude ratio, r, of the direct and short distantecho) for the evaluation. The system loops back to 604 where one or moreparameters are changed, and repeats steps 606-610 until a pulse waveformwith the best performance is found. At 614, the pulse waveform with thebest performance is stored.

It should be appreciated that the specific steps illustrated in FIG. 6provide a particular method of computing alternative pulse waveforms forDME/N according to an embodiment of the present invention. Othersequences of steps may also be performed according to alternativeembodiments. For example, alternative embodiments of the presentinvention may perform the steps outlined above in a different order.Moreover, the individual steps illustrated in FIG. 6 may includemultiple sub-steps that may be performed in various sequences asappropriate to the individual step. Furthermore, additional steps may beadded or removed depending on the particular applications. One ofordinary skill in the art would recognize many variations,modifications, and alternatives.

FIG. 7 is a simplified flowchart illustrating a method of computing afiltered asymmetric Gaussian pulse waveform for DME/N according to anembodiment of the invention. At 702, the system determines the range ofthe DME pulse width. At 704, the system starts the “pulse width” loop.At 706, the system determines the range of σ_(L). At 708, the systemstarts the “σ_(L)” loop. At 710, the system specifies time, T, for theleft-hand (i.e., the rising edge) and the right-hand (i.e., the fallingedge) sides of a filtered asymmetric Gaussian pulse. At 714, the systemcomputes σ_(R) using equation (9). At 716, the system generates afiltered asymmetric Gaussian pulse waveform using σ_(L), σ_(R), and T.At 718, the system determines the range of the smoothing window. At 720,the system starts the “window length” (WL) loop. At 722, the systemapplies the smoothing width WL on the asymmetric Gaussian pulsewaveform. At 724, the system determines the rise time, pulse width, andthe fall time of the resultant asymmetric Gaussian pulse waveform. At726, the system checks whether the resultant asymmetric Gaussian pulsewaveform meets the pulse shape requirements. If the answer is “no,” thesystem loops back to 720 where the window length WL is changed. If theanswer is “yes,” at 728, the system computes the channel power at 0.8MHz and 2 MHz from the nominal channel frequency f_(c). At 730, thesystem checks if the resultant asymmetric Gaussian pulse waveform meetsthe spectrum requirements. If the answer is “no,” the system loops backto 720 where the window length WL is changed. If the answer is “yes,” at732, the resultant asymmetric Gaussian pulse waveform is stored. At 734,the system loops back to 720 where the window length WL is changed untilall values of WL within the smoothing window range have been tried. At736, the system loops back to 708 where σ_(L) is changed until allvalues within the σ_(L) range have been tried. At 738, the system loopsback to 704 wherein the DME pulse width is changed until all valueswithin the DME pulse width range have been tried.

It should be appreciated that the specific steps illustrated in FIG. 7provide a particular method of computing a filtered asymmetric Gaussianpulse waveforms for DME/N according to an embodiment of the presentinvention. Other sequences of steps may also be performed according toalternative embodiments. For example, alternative embodiments of thepresent invention may perform the steps outlined above in a differentorder. Moreover, the individual steps illustrated in FIG. 7 may includemultiple sub-steps that may be performed in various sequences asappropriate to the individual step. Furthermore, additional steps may beadded or removed depending on the particular applications. One ofordinary skill in the art would recognize many variations,modifications, and alternatives.

FIG. 8 is a simplified flowchart illustrating a method of computing asmoothed trapezoidal pulse (STP) waveform for DME/N according to anembodiment of the invention. At 802, the system determines the rangesfor the baseline trapezoidal pulse waveform. At 804, the system startsthe trapezoidal parameter loop. At 806, the system determines the rangefor the DME pulse width. At 808, the system starts the “pulse width”loop. At 810, the system generates a baseline trapezoidal pulse waveformusing the given trapezoidal parameters and DME pulse width. At 812, thesystem determines the range for the smoothing window. At 814, the systemstarts the “window length” (WL) loop. At 816, the system applies thesmooth filter to the baseline trapezoidal pulse waveform. At 818, thesystem determines the rise time, pulse width, and the fall time of thesmoothed trapezoidal pulse waveform. At 820, the system checks whetherthe resultant smoothed trapezoidal pulse waveform meets the pulse shaperequirements. If the answer is “no,” the system loops back to 814 wherethe smoothing window length WL is changed. If the answer is “yes,” at822, the system computes the channel power at 0.8 MHz and 2 MHz from thenominal channel frequency f_(c). At 822, the system checks if theresultant smoothed trapezoidal pulse waveform meets the spectrumrequirements. If the answer is “no,” the system loops back to 814 wherethe smoothing window length is changed. If the answer is “yes,” at 826,the system stores the resultant smoothed trapezoidal pulse waveform. At828, the system loops back to 814 where the smoothing window length WLis changed until all values of WL within the smoothing window range havebeen tried. At 830, the system loops back to 808 where the DME pulsewidth is changed until all values within the DME pulse width range havebeen tried. At 832, the system loops back to 804 where the baselinetrapezoidal waveform parameters are changed until all values within thetrapezoid parameter range have been tried.

It should be appreciated that the specific steps illustrated in FIG. 8provide a particular method of computing a smoothed trapezoidal pulsewaveform for DME/N according to an embodiment of the present invention.Other sequences of steps may also be performed according to alternativeembodiments. For example, alternative embodiments of the presentinvention may perform the steps outlined above in a different order.Moreover, the individual steps illustrated in FIG. 8 may includemultiple sub-steps that may be performed in various sequences asappropriate to the individual step. Furthermore, additional steps may beadded or removed depending on the particular applications. One ofordinary skill in the art would recognize many variations,modifications, and alternatives.

FIG. 9 is a simplified flowchart illustrating a method of computing asmoothed concave hexagonal pulse (SCP) waveform for DME/N according toan embodiment of the invention. At 902, the system determines the rangesfor the baseline concave hexagonal pulse waveform. At 904, the systemstarts the concave hexagon parameter loop. At 906, the system determinesthe range for the DME pulse width. At 908, the system starts the “pulsewidth” loop. At 910, the system generates a baseline concave hexagonalpulse waveform using the given concave hexagon parameters and DME pulsewidth. At 912, the system determines the range for the smoothing window.At 914, the system starts the “window length” (WL) loop. At 916, thesystem applies the smooth filter to the baseline concave hexagonal pulsewaveform. At 918, the system determines the rise time, pulse width, andthe fall time of the smoothed concave hexagonal pulse waveform. At 920,the system checks whether the resultant smoothed concave hexagonal pulsewaveform meets the pulse shape requirements. If the answer is “no,” thesystem loops back to 914 where the smoothing window length WL ischanged. If the answer is “yes,” at 922, the system computes the channelpower at 0.8 MHz and 2 MHz from the nominal channel frequency f_(c). At922, the system checks if the resultant smoothed concave hexagonal pulsewaveform meets the spectrum requirements. If the answer is “no,” thesystem loops back to 914 where the smoothing window length is changed.If the answer is “yes,” at 926, the system stores the resultant smoothedconcave hexagonal pulse waveform. At 928, the system loops back to 914where the smoothing window length WL is changed until all values of WLwithin the smoothing window range have been tried. At 930, the systemloops back to 908 where the DME pulse width is changed until all valueswithin the DME pulse width range have been tried. At 932, the systemloops back to 904 where the baseline concave hexagonal waveformparameters are changed until all values within the concave hexagonparameter range have been tried.

It should be appreciated that the specific steps illustrated in FIG. 9provide a particular method of computing a smoothed concave hexagonalpulse waveform for DME/N according to an embodiment of the presentinvention. Other sequences of steps may also be performed according toalternative embodiments. For example, alternative embodiments of thepresent invention may perform the steps outlined above in a differentorder. Moreover, the individual steps illustrated in FIG. 9 may includemultiple sub-steps that may be performed in various sequences asappropriate to the individual step. Furthermore, additional steps may beadded or removed depending on the particular applications. One ofordinary skill in the art would recognize many variations,modifications, and alternatives.

FIG. 10 compares the resultant pulse shapes provided by the methodsdescribed herein along with the standard Gaussian pulse. The key pulseshape parameters of the pulses provided by embodiments of the presentinvention are listed in Table 3. From FIG. 10 and Table 3, two pulseshape characteristics for a better time-of-arrival (TOA) measurement canbe identified: the fast rise time and narrow width around the peak. Thetwo characteristics are useful for noise suppression and multipathmitigation among other performance parameters.

TABLE 3 Parameters of the DME/N Alternative Pulses Gaussian STP SCP AGPRise Time (μs) 2.5 1.50 1.50 1.68 Width (μs) 3.5 3.30 3.09 3.10 FallTime (μs) 2.5 2.94 2.48 2.76

The alternative pulses illustrated in FIG. 10 yield the most TOAmeasurement enhancement in each approach under the test of noise andmultipath. The TOA performance enhancement is evaluated by injectingrandom noise and multipath to each candidate alternative pulse andmeasuring the statistics of the TOA differences resulting from addingthe noise or multipath.

Table 4 lists the each test condition and the TOA performance of thevarious pulses in meters. The statistics (1σ) for the test under noiseuses 10,000 samples. r is the peak amplitude ratio of the direct andshort distant echoes. The phase difference between the direct and theecho is zero for all the cases. The TOA error statistics for the echotest is the Root-Mean-Square since the errors are mostly positivevalues. The performance of the Gaussian pulse is also listed and used asthe reference performance. The percentage values show the improvementsof the TOA errors over the traditional Gaussian pulse.

TABLE 4 Time of Arrival Errors under Noise and Multipath in Meters ofthe Three Optimal Alternative Pulses Gaussian STP SCP AGP Noise 10.67 6.56  6.62  6.83 (SNR = 25 dB) (39%) (38%) (36%) Noise 5.91  3.58  3.71 3.79 (SNR = 30 dB) (39%) (37%) (36%) Noise 1.85  1.15  1.16  1.19 (SNR= 40 dB) (38%) (38%) (36%) Echo 23.57 15.32 13.71 15.03 (r = 0.3) (35%)(42%) (36%) Echo 31.21 20.92 18.41 20.45 (r = 0.4) (33%) (41%) (34%)Echo 38.82 27.17 23.54 26.26 (r = 0.5) (30%) (39%) (32%)

Table 4 shows that the noise suppression performance of the STP isslightly better than the SCP. The difference is less than 13 cm at most.However, the multipath mitigation of the SCP is superior to the othersand at least 1.61 meters better than the STP.

FIG. 11 shows the TOA errors with respect to the given multipath delay.The SCP has the lowest peak of the error and the short multipath impactranges. Therefore, the SCP overall provides the best performance amongthe three candidates. The optimal SCP approximately has 15 dB margin of500 kHz band channel power at 800 kHz and 2 MHz from a DME centerfrequency.

FIG. 12 compares the power spectrums of the optimal SCP and Gaussianpulse against the DME spectrum envelope mask. The power spectrum of theoptimal SCP appears very close to the mask around 600 kHz from thecenter frequency but is actually below the mask over the given frequencyrange.

Note that the values of the TOA errors under noise and multipath couldbe different with respect to a TOA estimation algorithm that is notdiscussed in this disclosure.

The DME accuracy improvement can be improved (e.g., maximized) when theSCP is implemented in the ground DME transponder and airborneinterrogator together. To enable the implementation, the SCP couldeasily be implemented via software upgrades in DME ground stationequipment currently being procured by the FAA. Similar software upgradesto DME avionics may be possible with current state-of-the-art DME/DMEavionics. For legacy interrogators, the range accuracy improvement canbenefit from ground to air portion of the enhancement.

When the SCP is uploaded to the DME ground station equipment, it couldbe distorted through various processes in the transmitter such as pulseshaping and power amplification. The largest distortion may be caused bynonlinear RF High Power Amplifiers (HPAs). Although such distortionswould have little effect on pulse shape and corresponding rangeaccuracy, if not managed correctly, it could broaden frequency spectrumoutput (known as ‘spectral regrowth’) and cause co-channel interference.Such co-channel interference could require mitigation through areduction in DME ground station transmitter power and result in areduction in service volume for each DME site. The SCP design hasapproximately 15 dB margin to account for the possible spectral growth.This margin is expected to be sufficient. If some additional room forthe spectral growth is needed, a pre-distortion of the alternative pulsecan be used. The pre-distortion corrects the baseline pulse shape beforemodulation, up-conversion, and amplification thereby creating an outputsignal closer to the desired pulse shape.

FIG. 13 is a simplified flowchart illustrating a method for measuringdistance according to an embodiment of the invention in association withthe system in FIG. 18. At 1302, an airborne interrogator 1804 transmitsa first pair of RF pulses 1806. The RF pulses in the first pair of RFpulses 1806 are temporally separated from each other by a first timeinterval. Each of the RF pulses in the first pair of RF pulses has afirst pulse waveform. At 1304, the airborne interrogator 1804 receives asecond pair of RF pulses 1808 transmitted by a ground transponder 1812(e.g., using the antenna 1810 associated with the ground transponder1812, etc.) after the ground transponder 1812 has received the firstpair of RF pulses 1806 transmitted from the airborne interrogator 1804.The RF pulses in the second pair of RF pulses 1808 are temporallyseparated from each other by a second time interval. Each of the RFpulses in the second pair of RF pulses 1808 has a second pulse waveformcharacterized by a filtered asymmetric Gaussian function. At 1306, theairborne interrogator 1804 determines an elapsed time betweentransmitting the first pair of RF pulses 1806 and receiving the secondpair of RF pulses 1808. At 1308, the airborne interrogator 1804determines a distance between the airborne interrogator 1804 and theground transponder 1812 based on at least the elapsed time.

It should be appreciated that the specific steps illustrated in FIG. 13provide a particular method for measuring distance according to anembodiment of the present invention. Other sequences of steps may alsobe performed according to alternative embodiments. For example,alternative embodiments of the present invention may perform the stepsoutlined above in a different order. Moreover, the individual stepsillustrated in FIG. 13 may include multiple sub-steps that may beperformed in various sequences as appropriate to the individual step.Furthermore, additional steps may be added or removed depending on theparticular applications. One of ordinary skill in the art wouldrecognize many variations, modifications, and alternatives.

FIG. 14 is a simplified flowchart illustrating a method for measuringdistance according to an embodiment of the invention. At 1402, anairborne interrogator transmits a first pair of RF pulses. The RF pulsesin the first pair of RF pulses are temporally separated from each otherby a first time interval. Each of the RF pulses in the first pair of RFpulses has a first pulse waveform. At 1404, the airborne interrogatorreceives a second pair of RF pulses transmitted by a ground transponderafter the ground transponder has received the first pair of RF pulsestransmitted from the airborne interrogator. The RF pulses in the secondpair of RF pulses are temporally separated from each other by a secondtime interval. Each of the RF pulses in the second pair of RF pulses hasa second pulse waveform characterized by a smoothed trapezoidalfunction. The baseline trapezoidal function is characterized by a firstsegment having a first positive slope, a second flat segment, and athird segment having a second negative slope. The absolute value of thefirst positive slope is greater than the absolute value of the secondnegative slope. At 1406, the airborne interrogator determines an elapsedtime between transmitting the first pair of RF pulses and receiving thesecond pair of RF pulses. At 1408, the airborne interrogator determinesa distance between the airborne interrogator and the ground transponderbased on at least the elapsed time.

It should be appreciated that the specific steps illustrated in FIG. 14provide a particular method for measuring distance according to anembodiment of the present invention. Other sequences of steps may alsobe performed according to alternative embodiments. For example,alternative embodiments of the present invention may perform the stepsoutlined above in a different order. Moreover, the individual stepsillustrated in FIG. 14 may include multiple sub-steps that may beperformed in various sequences as appropriate to the individual step.Furthermore, additional steps may be added or removed depending on theparticular applications. One of ordinary skill in the art wouldrecognize many variations, modifications, and alternatives.

FIG. 15 is a simplified flowchart illustrating a method for measuringdistance according to an embodiment of the invention. At 1502, anairborne interrogator transmits a first pair of RF pulses. The RF pulsesin the first pair of RF pulses are temporally separated from each otherby a first time interval. Each of the RF pulses in the first pair of RFpulses has a first pulse waveform. At 1504, the airborne interrogatorreceives a second pair of RF pulses transmitted by a ground transponderafter the ground transponder has received the first pair of RF pulsestransmitted from the airborne interrogator. The RF pulses in the secondpair of RF pulses are temporally separated from each other by a secondtime interval. Each of the RF pulses in the second pair of RF pulses hasa second pulse waveform characterized by a smoothed concave hexagonalfunction. The baseline concave hexagonal function is characterized by afirst segment having a first positive slope, a second flat segment, athird segment having a second negative slope, a fourth segment having athird negative slope, and a fifth segment having a fourth negativeslope. The absolute value of the third negative slope is less than theabsolute value of the second negative slope. At 1506, the airborneinterrogator determines an elapsed time between transmitting the firstpair of RF pulses and receiving the second pair of RF pulses. At 1508,the airborne interrogator determines a distance between the airborneinterrogator and the ground transponder based on at least the elapsedtime.

It should be appreciated that the specific steps illustrated in FIG. 15provide a particular method for measuring distance according to anembodiment of the present invention. Other sequences of steps may alsobe performed according to alternative embodiments. For example,alternative embodiments of the present invention may perform the stepsoutlined above in a different order. Moreover, the individual stepsillustrated in FIG. 15 may include multiple sub-steps that may beperformed in various sequences as appropriate to the individual step.Furthermore, additional steps may be added or removed depending on theparticular applications. One of ordinary skill in the art wouldrecognize many variations, modifications, and alternatives.

FIG. 16 is a simplified flowchart illustrating a method for measuringdistance according to an embodiment of the invention. At 1602, anairborne interrogator transmits a first pair of RF pulses. The RF pulsesin the first pair of RF pulses are temporally separated from each otherby a first time interval. Each of the RF pulses in the first pair of RFpulses has a first pulse waveform. At 1604, the airborne interrogatorreceives a second pair of RF pulses transmitted by a ground transponderafter the ground transponder has received the first pair of RF pulsestransmitted from the airborne interrogator. The RF pulses in the secondpair of RF pulses are temporally separated from each other by a secondtime interval. Each of the RF pulses in the second pair of RF pulses hasa second pulse waveform characterized by a smoothed concave polygonalfunction. The baseline concave polygonal function is characterized by atleast a first segment having a first positive slope, a second flatsegment, a third segment having a second negative slope, a fourthsegment having a third negative slope, and a fifth segment having afourth negative slope. The absolute value of the third negative slope isless than the absolute value of the second negative slope. At 1606, theairborne interrogator determines an elapsed time between transmittingthe first pair of RF pulses and receiving the second pair of RF pulses.At 1608, the airborne interrogator determines a distance between theairborne interrogator and the ground transponder based on at least theelapsed time.

In some embodiments, the second pulse waveform may be characterized by awaveform function. For example, the waveform function can include afiltered asymmetric Gaussian function or a smoothed trapezoidalfunction. The waveform function may be obtained by applying a smoothingoperation on the trapezoidal function. The filtered asymmetric Gaussianfunction may be characterized by a rise time, a fall time, and a pulsewidth. The rise time may be greater than or equal to about 1.5 μs andless than or equal to about 3.0 μs, the fall time may be greater than orequal to about 2.0 μs and less than or equal to about 3.0 μs, and thepulse width may be greater than or equal to about 3.0 μs and less thanor equal to about 4.0 μs. The filtered asymmetric Gaussian function maybe characterized by a standard deviation on a rising edge that isgreater than or equal to about 0.77 μs and less than or equal to about1.77 μs, and a standard deviation on a falling edge that is greater thanor equal to about 0.90 μs and less than or equal to about 1.78 μs. Thewaveform function may be a smoothed trapezoidal function, and thesmoothed trapezoidal function may be characterized by a first segmenthaving a first positive slope, a second flat segment, and a thirdsegment having a second negative slope, an absolute value of the firstpositive slope being greater than an absolute value of the secondnegative slope. The airborne interrogator may measure a slant range bythe elapsed time between transmitting the first pair of RF pulses andreceiving the second pair of RF pulses. The first pair of RF pulses maybe transmitted at a power of more than about 800 Watts, including 1,000Watts.

It should be appreciated that the specific steps illustrated in FIG. 16provide a particular method for measuring distance according to anembodiment of the present invention. Other sequences of steps may alsobe performed according to alternative embodiments. For example,alternative embodiments of the present invention may perform the stepsoutlined above in a different order. Moreover, the individual stepsillustrated in FIG. 16 may include multiple sub-steps that may beperformed in various sequences as appropriate to the individual step.Furthermore, additional steps may be added or removed depending on theparticular applications. One of ordinary skill in the art wouldrecognize many variations, modifications, and alternatives.

FIG. 17 is a simplified flowchart illustrating a method for measuringdistance according to an embodiment of the invention. At 1702, a groundtransponder receives a first pair of RF pulses transmitted from anairborne interrogator. The RF pulses in the first pair of RF pulses aretemporally separated from each other by a first time interval. Each ofthe RF pulses in the first pair of RF pulses has a first pulse waveform.At 1704, the ground transponder transmits a second pair of RF pulsesafter receiving the first pair of RF pulses. The RF pulses in the secondpair of RF pulses are temporally separated from each other by a secondtime interval. Each of the RF pulses in the second pair of RF pulses hasa second pulse waveform characterized by a smoothed concave polygonalfunction. The baseline concave polygonal function is characterized by atleast a first segment having a first positive slope, a second flatsegment, a third segment having a second negative slope, a fourthsegment having a third negative slope, and a fifth segment having afourth negative slope. The absolute value of the third negative slope isless than the absolute value of the second negative slope. The secondpair of RF pulses is to be received by the airborne interrogator,thereby a distance between the airborne interrogator and the groundtransponder is determined based on at least an elapsed time betweentransmitting the first pair of RF pulses and receiving the second pairof RF pulses. In alternative embodiments of the present invention, thesecond pulse waveform is characterized by a filtered asymmetric Gaussianfunction, a smoothed trapezoidal function, a smoothed concave hexagonalfunction, or the like, as described throughout this disclosure.

It should be appreciated that the specific steps illustrated in FIG. 17provide a particular method for measuring distance according to anembodiment of the present invention. Other sequences of steps may alsobe performed according to alternative embodiments. For example,alternative embodiments of the present invention may perform the stepsoutlined above in a different order. Moreover, the individual stepsillustrated in FIG. 17 may include multiple sub-steps that may beperformed in various sequences as appropriate to the individual step.Furthermore, additional steps may be added or removed depending on theparticular applications. One of ordinary skill in the art wouldrecognize many variations, modifications, and alternatives.

Embodiments of the present invention provide alternative DME/N pulseshapes that can provide significant range accuracy improvement over thestandard Gaussian pulse without a loss of coverage. As discussed above,the smoothed concave hexagonal pulse (SCP) provides significantimprovement in range accuracy in comparison with conventional pulses.The SCP is compliant with the pulse shape and spectrum requirements ofthe current DME specification. From the simulation of noise and shortdistant echoes, the SCP showed range accuracy improvement about 37˜38%against the noise with 25˜40 dB SNR and about 39˜42% improvement againstthe constructive short distance echoes with the direct and echoamplitude ratio of 0.3˜0.5.

It is also understood that the examples and embodiments described hereinare for illustrative purposes only and that various modifications orchanges in light thereof will be suggested to persons skilled in the artand are to be included within the spirit and purview of this applicationand scope of the appended claims.

What is claimed is:
 1. A method for measuring distance, the methodcomprising: transmitting a first RF pulse from an airborne interrogator,wherein the first RF pulse has a first pulse waveform; receiving, at theairborne interrogator, a second RF pulse transmitted by a groundtransponder after the ground transponder has received the first RF pulsetransmitted by the airborne interrogator, wherein the second RF pulsehas a second pulse waveform characterized by a smoothed concavehexagonal function formed by: generating a single pulse having a firstsegment connected to a second flat segment connected to a third segmentconnected to a fourth segment connected to a fifth segment, the firstsegment having a first positive slope, the third segment having a secondnegative slope, the fourth segment having a third negative slope, andthe fifth segment having a fourth negative slope, wherein the thirdnegative slope is steeper than the second negative slope, and applying asmoothing operation to the single pulse; determining an elapsed timebetween transmitting the first RF pulse and receiving the second RFpulse; and determining a distance between the airborne interrogator andthe ground transponder based on at least the elapsed time.
 2. The methodof claim 1 wherein the first positive slope is greater than 0.7 μs⁻¹. 3.The method of claim 1 wherein the absolute value of the second negativeslope is greater than 0.7 μs⁻¹.
 4. The method of claim 1 wherein theabsolute value of the third negative slope is less than an absolutevalue of the fourth negative slope.
 5. The method of claim 1 wherein thesecond RF pulse has a power of more than 800 Watts.
 6. The method ofclaim 1 further comprising: receiving a third RF pulse transmitted bythe ground transponder; and determining a standard deviation of one ormore segments from the second RF pulse and third RF pulse.
 7. A methodfor distance measuring comprising: transmitting a first RF pulse from anairborne interrogator, wherein the first RF pulse has a first pulsewaveform; receiving, at the airborne interrogator, a second RF pulsetransmitted by a ground transponder after the ground transponder hasreceived the first RF pulse transmitted by the airborne interrogator,wherein the second RF pulse has a second pulse waveform characterized bya smoothed concave polygonal function formed by: generating a singlepulse having a first segment connected to a second flat segmentconnected to a third segment connected to a fourth segment connected toa fifth segment, the first segment having a first positive slope, thethird segment having a second negative slope, the fourth segment havinga third negative slope, and the fifth segment having a fourth negativeslope, wherein the third negative slope is steeper than the secondnegative slope, and applying a smoothing operation to the single pulse;determining an elapsed time between transmitting the first RF pulse andreceiving the second RF pulse; and determining a distance between theairborne interrogator and the ground transponder based on at least theelapsed time.
 8. The method of claim 7 wherein the first pulse waveformcomprises the smoothed concave polygonal function.
 9. The method ofclaim 7 wherein the first positive slope is greater than 0.7 μs⁻¹. 10.The method of claim 7 wherein the absolute value of the second negativeslope is greater than 0.7 μs⁻¹.
 11. The method of claim 7 wherein theabsolute value of the third negative slope is less than an absolutevalue of the fourth negative slope.
 12. The method of claim 7 whereinthe second RF pulse has a power of more than 800 Watts.
 13. The methodof claim 7 further comprising: receiving a third RF pulse transmitted bythe ground transponder; and determining a standard deviation of one ormore segments from the second RF pulse and third RF pulse.
 14. A methodof measuring distance, the method comprising: receiving, at a groundtransponder, a first RF pulse transmitted from an airborne interrogator,wherein the first RF pulse has a first pulse waveform; and generating,at the ground transponder and after receiving the first RF pulse, asecond RF pulse, wherein the second RF pulse has a second pulse waveformcharacterized by a smoothed concave polygonal function formed by:generating a single pulse having a first segment connected to a secondflat segment connected to a third segment connected to a fourth segmentconnected to a fifth segment, the first segment having a first positiveslope, the third segment having a second negative slope, the fourthsegment having a third negative slope, and the fifth segment having afourth negative slope, wherein the third negative slope is steeper thanthe second negative slope, and applying a smoothing operation to thesingle pulse to generate the second RF pulse, and transmitting thesecond RF pulse to the airborne interrogator, wherein the second RFpulse is received by the airborne interrogator, and a distance betweenthe airborne interrogator and the ground transponder is determined basedon at least an elapsed time between transmitting the first RF pulse andreceiving the second RF pulse.
 15. The method of claim 14 wherein thesmoothing operation is performed by a moving average filter, a splinefilter, or a zero phase forward and backward digital filter.
 16. Asystem for distance measuring comprising: an airborne interrogatoroperable to transmit a first RF pulse, wherein the first RF pulse has afirst pulse waveform; and a ground transponder operable to receive thefirst RF pulse transmitted by the airborne interrogator, generate asecond RF pulse after receiving the first RF pulse, wherein the secondRF pulse has a second pulse waveform characterized by a smoothed concavepolygonal function formed by: generating a single pulse having a firstsegment connected to a second flat segment connected to a third segmentconnected to a fourth segment connected to a fifth segment, the firstsegment having a first positive slope, the third segment having a secondnegative slope, the fourth segment having a third negative slope, andthe fifth segment having a fourth negative slope, wherein the thirdnegative slope is steeper than the second negative slope, applying asmoothing operation on the single pulse to generate the second RF pulse,and transmitting the second RF pulse to the airborne interrogator,wherein the airborne interrogator is further operable to receive thesecond RF pulse transmitted by the ground transponder, whereby adistance between the airborne interrogator and the ground transponder isdetermined based on at least an elapsed time between transmitting thefirst RF pulse and receiving the second RF pulse.
 17. The system ofclaim 16 wherein the airborne interrogator measures a slant range by theelapsed time between transmitting the first RF pulse and receiving thesecond RF pulse.
 18. The system of claim 16 wherein the first RF pulseare transmitted at a power of more than ab-out 800 Watts.
 19. The systemof claim 16 wherein the first RF pulse or second RF pulse include one ormore of the following: a rise time of 1.56 μs, a fall time of 2.30 μs,and pulse width of 3.06 μs.
 20. The system of claim 16 wherein the firstRF pulse or second RF pulse are enabled to transmit at least 100nautical miles.